The aim of ridge regression is to \( \min_{w} ||y - Xw||^2_2 + \alpha||w||^2_2 \), therefore \( \alpha \) stands for how much ridge regression should prevent overfitting.
From that fact, with smaller values for \( \alpha \) the ridge regression overfits the dataset, ending up with an approximation function quite close to the original one, while with higher values for it the ridge regression ends up with an approximation function very different from the original one.
A special case is when \( \alpha = 0 \), since we want the ridge regression to overfit as much as possible the dataset.
Here you can find the notebook with all the code: https://colab.research.google.com/drive/15K0qcUlYjiUDtrxGABdBpkN312YNq0ai?usp=sharing